Related papers: Development Processes
We consider the simultaneous movement of finitely many colored points in space, calling it a spatial sorting process. The name suggests a purpose that drives the collection to a configuration of increased or decreased order. Mapping such a…
Evolutionary change over time in the context of data pipelines is certain, especially with regard to the structure and semantics of data as well as to the pipeline operators. Dealing with these changes, i.e. providing long-term maintenance,…
Suppose $(f,\mathcal{X},\mu)$ is a measure preserving dynamical system and $\phi \colon \mathcal{X} \to \mathbb{R}$ a measurable function. Consider the maximum process $M_n:=\max\{X_1 \ldots,X_n\}$, where $X_i=\phi\circ f^{i-1}$ is a time…
Developmental patterning comprises processes that range from purely instructed, where external signals specify cell fates, to fully self-organized, where spatial patterns emerge autonomously through cellular interactions. We propose that…
Potentialism is the view that objects are successively generated in an incompletable process. A strict version of the view adds that truths are successively determined. Strict potentialism can be analyzed using two modalities: one for the…
Many AI problems, in robotics and other domains, are goal-directed, essentially seeking a trajectory leading to some goal state. In such problems, the way we choose to represent a trajectory underlies algorithms for trajectory prediction…
Learning systems acquire structured internal representations from data, yet classical information-theoretic results state that deterministic transformations do not increase information. This raises a fundamental question: how can learning…
Modern information systems are changing the idea of "data processing" to the idea of "concept processing", meaning that instead of processing words, such systems process semantic concepts which carry meaning and share contexts with other…
This article presents a general description of dynamical systems using the language of enriched functors and enriched natural transformations. This framework is essential to establish the equivalence of three descriptions of dynamics -- a…
We consider a set-theoretic version of mereology based on the inclusion relation $\subseteq$ and analyze how well it might serve as a foundation of mathematics. After establishing the non-definability of $\in$ from $\subseteq$, we identify…
According to the math tea argument, there must be real numbers that we cannot describe or define, because there are uncountably many real numbers, but only countably many definitions. And yet, the existence of pointwise-definable models of…
A new account of parameter setting during grammatical acquisition is presented in terms of Generalized Categorial Grammar embedded in a default inheritance hierarchy, providing a natural partial ordering on the setting of parameters.…
Dynamical systems are a broad class of mathematical tools used to describe the evolution of physical and computational processes. Traditionally these processes model changing entities in a static world. Picture a ball rolling on an empty…
In semantic technologies, the shared common understanding of the structure of information among artifacts (people or software agents) can be realized by building an ontology. To do this, it is imperative for an ontology builder to answer…
Do Large Language Models (LLMs) genuinely grasp the compositional semantics of events, or do they rely on surface-level probabilistic heuristics? We investigate the Imperfective Paradox, a logical phenomenon where the past progressive…
Topic models are probabilistic models for discovering topical themes in collections of documents. In real world applications, these models provide us with the means of organizing what would otherwise be unstructured collections. They can…
The idea that there are any large-scale trends in the evolution of biological organisms is highly controversial. It is commonly believed, for example, that there is a large-scale trend in evolution towards increasing complexity, but…
A conceptual system with rich connotation is key to improving the performance of knowledge-based artificial intelligence systems. While a conceptual system, which has abundant concepts and rich semantic relationships, and is developable,…
I assess various proposals for the source of the intuition that there is something problematic about contextuality, ultimately concluding that contextuality is best thought of in terms of fine-tuning. I then argue that as with other…
As a first step toward realizing a dynamical system that evolves while spontaneously determining its own rule for time evolution, function dynamics (FD) is analyzed. FD consists of a functional equation with a self-referential term, given…